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Journals and Conferences

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive.… (More)

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur… (More)

For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young… (More)

Inspired by the k-inversion statistic for LLT polynomials, we define a k-inversion number and k-descent set for words. Using these, we define a new statistic on words, called the k-major index, that… (More)

Dual equivalence puts a crystal-like structure on linear representations of the symmetric group that affords many nice combinatorial properties. In this talk, we extend this theory to type B, putting… (More)

In the early 1990s, Garsia and Haiman conjectured that the dimension of the Garsia-Haiman module Rμ is n!, and they showed that the resolution of this conjecture implies the Macdonald Positivity… (More)